Spot check

An illuminating parallel between cat coats and vegetation patterns

TIGER bush gets its name because the bands and patches of trees and shrubs found in arid climes often grow in ways that, viewed from above, look like the stripes and spots on feline coats. If what Bonni Kealy of Washington State University told a meeting of the American Mathematical Society and the Mathematical Association of America, held in Boston on January 4th-7th, is right, the moniker is more apt than its inventors could have known.

Dr Kealy and her colleague David Wollkind believe that in both cases nature is using the same copybook: one written in algebra. (The chapter on non-linear partial differential equations, to be precise.) Animals' variegated coats are thought to be the result of what is known as a reaction-diffusion process. This is a tug-of-war between two chemicals' tendency to spread throughout an environment and their propensity to react in such a way that each turns into the other.

Such a contest can lead to stable, and often complex, arrangements of the chemicals' relative concentrations. If the environment being spread through is an animal embryo and the reagents are hormones that trigger the differentiation of the body's pigment-producing cells, the upshot is a distinct pattern of pigmentation. Since animal coats and tiger-bush patterns look alike, Dr Kealy and Dr Wollkind reasoned that the ways they are produced might be akin, too—at least mathematically.

To test their theory, the two researchers first needed to find ecological equivalents of the differentiation-triggering chemicals: two things whose relative concentrations affect the shape of patches of vegetation and which like both to spread and to transmute into one another. Water and plants, it seems, fit the bill nicely. Each is essential to the development of tiger-bush formations. Each tends to spread: water by seeping across the soil; plants by ejecting seeds or spores. Less obviously, each in effect turns into the other. Plants grow by taking water from the soil, and when a plant dies it frees water which it would otherwise consume.

This insight allowed Dr Kealy and Dr Wollkind to create equations that, once plugged into computer simulations of reaction-diffusion processes, produce all manner of lifelike tiger-bush schemes, including the most intricate sort. Earlier models, which tried to use water flow and plant growth to explain how the tiger bush got its stripes, failed to account for all but the simplest patterns. Dr Kealy's model, by contrast, is spot-on.